Problem: $-32 + (-34) + (-36) +... + (-778) + (-780)=$
Getting started We're dealing with an arithmetic series because the difference between terms is constant. That is, each term is $2$ less than the one before it. We need a formula to compute the sum of the terms. Formula for arithmetic series The sum $S_n$ of a finite arithmetic series is $S_n = \dfrac {\left(a_1 + a_n \right)}{2} \cdot n$ where $a_1$ is the first term, $a_n$ is the last term, and $n$ is the number of terms. What do we need to use the formula? The first term $(a_1 = {-32})$ and the last term $(a_n = {-780})$ are given in the question. We need to find $n$ (the number of terms). Step 1: Find $n$ (the number of terms) The sequence decreases by $(-32) - (-780) = 748$ from the first term to the last term. Because the sequence decreases by $2$ each time, it takes $\dfrac{748}{2} = 374$ terms to get from the first term to the last term. We still need to count the first term, so there are $374 + 1 = {375}$ terms in the sequence. In other words, $n = {375}$. Step 2: Find the sum $(S_n)$ of the series $\begin{aligned} S_n &= \dfrac {\left(a_1 + a_n \right)}{2} \cdot n \\\\ S_{{375}}&= \dfrac {\left({-32} + ({-780}) \right)}{2} \cdot {375} \\\\ S_{{375}} &= -406 \left(375\right) \\\\ S_{{375}} &= -152{,}250 \end{aligned}$ The answer $ -152{,}250 $